Is anyone aware of any of the Tanaim or Amoraim who had more than one wife (at the same time)? Not just technically married, but actually living together as husband and wife (or wives). I was once told that you will not find any that did.

No, I’m not aware of such a citation. But I have two tangential observations I’d like to make.

Chazal clearly talk about polygamy as if it were a going concern. This is not dispositive; they often talk about many areas of halacha as if these areas had current application regardless of whether they did in fact have current application. Still it’s interesting to see discussion of polygamy in which nobody suggests that polygamy is a dead letter. At Succah 27a4 someone asks R’ Eliezer about the correct way to fulfill the Succah obligations given that he (the one asking the question) has one wife in Tiberius and one in Tzipori; questions about polygamy arise at Kiddushin 50b3, Bava Basra 143a2, etc. In Tractate Yevamos (as for example Yevamos 65a3) the topic arises again and again; one of the major topics of the tractate is whether a given man and woman should perform a levirate marriage, given various relationships among the parties that can include the other wives of the deceased or surviving brother.

Where rabbis mention their own wives, the Gemara seems uncurious about the order of the marriages or how they ended. For example, we’re told (Avodah Zarah 20a3 #28, cf. Nedarim-50b Rishoinim) that Rabbi Akiva married the former Mrs. Turnus Rufus. The Gemara doesn’t seem to mind that elsewhere in Shas R’ Akiva married [Rachel] the daughter of a [Bar] Kalbua Savua (Nedarim 50a1, Kesubos 62b, Chagigah 12a5).

But I definitely agree that what's more striking is the seeming scarcity of polygamy during a period before the famous ban, with only a very few references in such an enormous record of life in the age of Chazal.

P.S. Some of my page numbers are ArtScroll-style, in which style the Vilna page number is followed by a digit reflecting the number of pages of translation. For example, Succah 27a4 refers to Vilna Succah 27a, but page 4 in ArtScroll's translation of that page. This specificity might sometimes be useful even to someone uninterested in ArtScroll's translation, as a way of identifying a place on the daf.

"The Gemara doesn’t seem to mind that elsewhere in Shas R’ Akiva married [Rachel] the daughter of a [Bar] Kalbua Savua" Maybe its just two accounts. How do we know that the authors of either story know about the other?
– mevaqeshJun 11 '17 at 17:08

@mevaqesh I agree that we don't know whether the authors knew of both events. You might think that the details of R' Akiva's family life would have been better-known to Chazal (in that generation and later ones) than they are to me, but that would be just a hunch.
– ChaimJun 11 '17 at 17:14

@Double AA♦ I have no objection to that supposition. I was just commenting that although Moses613 and I are curious about the question, the Gemara seems not to be. It seems to me that if you found out that a married man had married again, it would be totally natural to ask "Isn't he already married?"
– ChaimJun 11 '17 at 17:21

@Double AA In other words, our response ("Isn't he already married?") is natural because in our world (at the moment) polygamy is not normal. In a world in which polygamy was normal you might expect people to do what the Gemara does: ascribe more than one wife to the same man without surprise.
– ChaimJun 11 '17 at 17:41